Site balance equation, catalytic

The reactor model adopted for describing the lab-scale experimental setup is an isothermal homogeneous plug-flow model. It is composed of 2NP + 2 ordinary differential equations of the type of Equation 16.11 with the initial condition of Equation 16.12, NP + 3 algebraic equations of the type of Equation 16.13, and the catalytic sites balance (Equation 16.14) ... 

The last equation is not independent of the others due to the site balance of Eq. (141) hence, in general, we have n-1 equations for a reaction containing n elementary steps. Note that steady state does not imply that surface concentrations are low. They just do not change with time. Hence, in the steady state approximation we can not describe time-dependent phenomena, but the approximation is sufficient to describe many important catalytic processes. 

For complex catalytic reactions requiring numerical analyses, it is useful to write the material balance equations for flow reactors in terms of molecular flow rates per active site (/ /, = Fi/Sr), which are denoted as molecular site velocities. For batch reactors, the number of gaseous molecules per active site (Ns,i = Ni /.SR) is used. (These normalized quantities are typically of the order of unity.) The batch reactor, CSTR, and PFR material balance equations become the following ... 

The molecular weight distribution can be calculated by solving the mass balance equations for monomer(s), initiator (catalytic sites), and polymeric species with different chain lengths. When quasisteady state assumption is applied to live polymers or propagating active centers, the molecular weight distribution of live polymers is often represented by the Schultz-Flory most probable distribution. However, the calculation of the chain length distribution of dead polymers is in general quite complicated. For some special cases such as... 

In these models, all reaction rates are proportional to the number of reaction sites hence it is natural to solve the stationary charge balance equation for the parameters applied potential difference appi and the ratio of catalytic sites a. 

There are also relationships between intermediates giving balance or conservation equations. For example, such an equation could relate the total concentration of intermediate species bound to a catalyst (enzyme). The enzyme could be then either in free form or bound to substrate, and the sum of these two forms is equal to the initial concentration of enzyme that was introduced in the system. For heterogeneous catalytic reactions, a balance equation relates the surface coverage of adsorbed species and vacant sites. If there are two types of sites on the surface, there would be two balance equations. It was shown by Horiuti that the number of basic routes P is determined by ... 

The computer-reconstructed catalyst is represented by a discrete volume phase function in the form of 3D matrix containing information about the phase in each volume element. Another 3D matrix defines the distribution of active catalytic sites. Macroporosity, sizes of supporting articles and the correlation function describing the macropore size distribution are evaluated from the SEM images of porous catalyst (Koci et al., 2006 Kosek et al., 2005). Spatially 3D reaction-diffusion system with low concentrations of reactants and products can be described by mass balances in the form of the following partial differential equations (Koci et al., 2006, 2007a). For gaseous components ... 

The main reaction i.e, benzene hydrogenation occuring inside porous Ni-catalyst pellets is accompanied by poisoning reaction in which the thiophene presented in the feed stream reacts irtevcrsibly with the catalytic active sites. An analysis was made assuming isothermal behaviour [7], the same effective diffusivity for reactant and poison and that the steady-state continuity equation represents a good approximation at all times [8,9]. Under these conditions the mass balances for benzene, thiophene and catalyst activity are... 

In general, a polymerization process model consists of material balances (component rate equations), energy balances, and additional set of equations to calculate polymer properties (e.g., molecular weight moment equations). The kinetic equations for a typical linear addition polymerization process include initiation or catalytic site activation, chain propagation, chain termination, and chain transfer reactions. The typical reactions that occur in a homogeneous free radical polymerization of vinyl monomers and coordination polymerization of olefins are illustrated in Table 2. 

Consequently, the reactor model is constituted by a system of N+1 equations, where N is the number of chemical species present in the system (NO, NO2, N2 and O2, neglecting the presence of N2O N = 4) and another unknown variable is pressure. The equations are one momentum balance (in the form of simplified Ergun Law), and four mass balance relationships. The presence of NO2 among the reaction products has been related to the catalytic activity of Cu-ZSM5 towards the oxidation of NO to NO2, as revealed by our previous investigation in similar experimental conditions [7], as well as by the present results (Fig. 1). It has been hypothesised that reaction (2) proceeds in parallel to NO decomposition, having not assumed that NO2 formation is responsible for copper reduction from Cu (inactive in decomposing NO) to Cu (the active site), as also proposed by some author [20-21,23]. 

A distinguishing feature of the new class of synthetic zeolites used in selective alkylation is a high silica/alumlna mole ratio, l.e., greater than 12. Since each aluminum has a net -1 charge, the presence of a cation is required to maintain ionic balance. This cation is an acidic proton, which is the catalytic site for alkylation to produce ethyltoluene (Equation 1). 

For catalytic reactions, one or more catalyst (site, enzyme) balances are required to derive a rate equation, with either the RLS approximation or the SSA. 

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